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- Title
Unnormalized differences between zeros of L-functions.
- Authors
Ford, Kevin; Zaharescu, Alexandru
- Abstract
We study a subtle inequity in the distribution of unnormalized differences between imaginary parts of zeros of the Riemann zeta function, which was observed by a number of authors. We establish a precise measure which explains the phenomenon, that the location of each Riemann zero is encoded in the distribution of large Riemann zeros. We also extend these results to zeros of more general $L$-functions. In particular, we show how the rank of an elliptic curve over $\mathbb{Q}$ is encoded in the sequences of zeros of other$L$-functions, not only the one associated to the curve.
- Subjects
ZETA functions; ELLIPTIC curves; ZERO (The number); MATHEMATICAL functions; MATHEMATICAL analysis; NUMERICAL analysis
- Publication
Compositio Mathematica, 2015, Vol 151, Issue 2, p230
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X14007659